The goal of the study is to determine the safety and possible effectiveness of various doses of autologous (one's own) stem cells, delivered with a needle into the regions of the leg with poor blood flow in patients with blocked leg arteries that results in claudication (pain when walking). Stem cells are primitive cells produced by the bone marrow that can develop into blood cells or other types of cells. In addition to determining whether this new approach is safe, the diagnostic tests may offer preliminary insights into the usefulness of this approach for treating intermittent claudication - the condition where areas in the leg are lacking enough oxygen and blood flow to keep the leg muscle working well, causing pain and cramping upon walking.